Cut triangulation effectively (find subtriangulation)

Question

I am working on terrain rendering tool currently. I have to cut a piece from a given Delaunay triangulation. Suppose following triangulation is given:

The red square depicts area to cut from the original triangulation, i.e. find sub triangulation which has the same points as the original triangulation plus points on the square's border.

Is there any kind efficient algorithm to perform such cut?

Answer 1

You need to use a constrained Delaunay triangulation.

The CGAL library for example provides an implementation in C++. As you talk about terrain, you should also look at this example.

If you are interested in a java or python implementation, some bindings written with SWIG are available here.